[ Astronomy & Space ] Open Question : What is the answer to life, the universe and everything?

[ Astronomy & Space ] Open Question : What is the answer to life, the universe and everything?

algorithm analysis – Space complexity of using a pairwise independent hash family

I’m trying to analyze the space complexity of using the coloring function $f$ which appears in “Colorful Triangle Counting and a MapReduce Implementation”, Pagh and Tsourakakis, 2011, https://arxiv.org/abs/1103.6073.

As far as I understand, $f:(n) rightarrow (N)$ is a hash function, that should be picked uniformly at random out of a pairwise independent hash functions family $H$. I have a few general questions:

  1. Does the space complexity required by $f$ is affected by the fact that $H$ is $k$-wise independent? Why? (if it does, then also- how?)
  2. What do we know about $|H|$? What if $H$ is $k$-wise independent?
  3. Is there a more space-efficient way to store $f$ than storing an $N times m$ matrix that maps each vertex to its color, using O($N m$) storage words?
  4. Does the total space complexity which is required in order to use $f$ as described in the paper is $|H| cdot O(text{space complexity of } f)$?

Best regards

root access – How can I get more internal space for apps?

I have read several places on this but the answers all seem to be the same. The problem is that I keep running out of space on my /data partition. The steps I’ve taken to fix this problem: move all apps that will function on sdcard to sdcard, also clear data on apps but the problem with this is that as soon as you open them again they act like a fresh install and then refill data.

My device stats 1gb /data partition 30gb ‘internal’ sdcard partition, Android 4.2.2 with root kernel 3.0.36+. Ideas I’ve had to fix this problem and the problems I faced attempting to use them:

  1. Repartition some of the /sdcard space to /data, problem is I can’t really find any specific instructions on how to do this and from what I have read I’m not really sure if I can because my “userdata” (/data) partition is at mtd6 and my “user” (/sdcard) partition is at mtd9 with “kpanic” and “system” at mtd 7 & 8 respectively, the guides mention mmc blocks instead of mtd which one seems to be an emulation of the other. I have seen other devices of the same model come from the factory with 2gb of /data storage.

  2. Move the /data/data contents of an app to sdcard and bind mount that location, problem is these directories always contain a /lib link thats points to wherever the apps installed package location is and this link can’t seem to be made, also not sure if I can make permissions right. As I understand it, when android installs an app to the sdcard it creates a small ext4 partition to contain the app package so I’m wondering if its possible to do something similar and then bind an apps /data/data assets to it.

Photos taking up space in General > iPhone Storage, but I don’t have any photos and iCloud Photos is disabled

so I recently was backing up my photos to google photos, and I usually clear everything from my photo library because it takes up space. I make sure to delete the recently deleted album as well, but I noticed that Photos still takes up space in iPhone Storage under General.

I’ve tried rebooting and resetting all settings, but it doesn’t seem to fix the problem. I disabled and deleted all of my photos in iCloud, so I don’t see how that could be the cause of this problem. I found a similar post but I’ve tried everything suggested except for restoring the iPhone.

So before I go ahead and restore my phone, I just wanted to make sure if there’s anything else I could try since that post is pretty old.

Here’s a screenshot of the issue:
enter image description here

[ Politics ] Open Question : If Hitler and the Nazis won WWII would Europeans have colonized space by now?

[ Politics ] Open Question : If Hitler and the Nazis won WWII would Europeans have colonized space by now?

algorithm analysis – Analyzing space complexity of passing data to function by reference

I have some difficulties with understanding the space complexity of the following algorithm.
I’ve solved this problem subsets on leetcode. I understand why solutions’ space complexity would be O(N * 2^N), where N – the length of the initial vector. In all those cases all the subsets (vectors) are passed by value, so we contain every subset in the recursion stack. But i passed everything by reference. This is my code:

class Solution {
public:
vector<vector<int>> result;
void rec(vector<int>& nums, int &position, vector<int> &currentSubset) {
    if (position == nums.size()) {
        result.push_back(currentSubset);
        return;
    }
    
    currentSubset.push_back(nums(position));
    position++;
    rec(nums, position, currentSubset);
    currentSubset.pop_back();
    rec(nums, position, currentSubset);
    position--;
}

vector<vector<int>> subsets(vector<int>& nums) {
    vector <int> currentSubset;
    int position = 0;
    rec(nums, position, currentSubset);
    return result;
}
};

Would the space complexity be O(N)? As far as i know, passing by reference doesn’t allocate new memory, so every possible subset would be contained in the same vector, which was created before the recursion calls.

I would also appreciate, if you told me how to estimate the space complexity, when working with references in general. Those are the only cases, where i hesitate about the correctness of my reasonings.

Thank you.

probability theory – Show that the adjoint of this Markov semigroup eventually preserves a Wasserstein space

Let $E$ be a separable $mathbb R$-Banach space, $mathcal M_1$ denote the set of probaiblity measures on $(E,mathcal B(E))$, $(kappa_t)_{tge0}$ be a Markov semigroup on $(E,mathcal B(E))$ and $rho$ be a metric on $E$ with $$(mukappa_totimesdelta_0)rhole cint v^{lambda(t)}:{rm d}mutag1$$ for all $tge0$ and $muinmathcal M_1$ for some $cge0$, some continuous $v:Eto(1,infty)$ and some nonincreasing $lambda:(0,infty)to(0,1)$ with $lambda(t)xrightarrow{ttoinfty}0$.

Let $$mathcal S^1:={muinmathcal M_1:exists yin E:(muotimesdelta_y)rho<infty}$$ denote the Wasserstein space associated to $rho$. Are we able to conclude that, if $(kappa_t)_{tge0}$ has an invariant measure, it must belong to $mathcal S^1$?

My idea is to show that there is a $t_0ge0$ such that the adjoint$^1$ $kappa_t^ast$ maps $mathcal M_1$ to $mathcal S^1$ for all $tge t_0$.

I’m only able to prove something weaker: Let $muinmathcal M_1$. By the monotone convergence theorem, $$(mukappa_totimesdelta_0)rhoxrightarrow{ttoinfty}ctag2,$$ but I’m not sure if this is sufficient for the desired conclusion.


$^1$ $kappa_t^astmu:=mukappa_t$.

Why the space key does not work,

Why the space keyboard does not work, I want to use the space key, I must press shift+space in windows 10. Could you tell me how to solve this problem?

Thanks a lot!

Jason Cai

Space consumed by an OS

My 64 GB new phone shows only 50 GB of free space. Is there a problem in my phone or the OS is really taking up 14GB of space ?

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